Some results on the generalized Drazin inverse of operator matrices

The generalized Drazin inverse M d of a 2 × 2 operator matrix is considered, where A ∈ ℬ(X) and D ∈ ℬ(Y) are generalized Drazin invertible. Expressions for the generalized Drazin inverse M d of operator matrix M in terms of the individual blocks A, B, C, D, A d and D d are derived under some conditions.

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